LOCAL SYMPLECTIC INVARIANTS FOR CURVES-Reference-Cited by-同舟云学术

LOCAL SYMPLECTIC INVARIANTS FOR CURVES

Published:2009-04 Issue:02 Volume:11 Page:165-183
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

KAMRAN NIKY¹,OLVER PETER²,TENENBLAT KETI³

Affiliation:

1. Department of Mathematics and Statistics, McGill University, Montreal, QC, H3A 2K6, Canada

2. School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA

3. Departamento de Matemática, Universidade de Brasília, Brasília 70910 DF, Brazil

Abstract

We consider curves in ℝ2n endowed with the standard symplectic structure. We introduce the concept of symplectic arc length for curves. We construct an adapted symplectic Frenet frame and we define 2n - 1 local differential invariants that we call symplectic curvatures of the curve. We prove that up to a rigid symplectic motion of ℝ2n, there exists a unique curve with prescribed symplectic curvatures. We characterize the curves in ℝ4 with constant symplectic curvatures.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199709003326

Reference12 articles.

1. Geometric invariants of fanning curves

2. Introduction to the variational bicomplex

3. Differential invariants for symplectic Lie algebras realized by boson operators

4. Affine Geometry, Curve Flows, and Invariant Numerical Approximations

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